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Numerically Stable Methods for the Computation of Exit Rates in Markov Chains

Twisting the Alive Particle Filter

Characterization and Enumeration of Certain Classes of Tenable Pólya Urns Grown by Drawing Multisets of Balls

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On the Laplace Transform of the Lognormal Distribution

A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities

Birth and Death Chains on Finite Trees: Computing their Stationary Distribution and Hitting Times

Analysis and Approximation of a Stochastic Growth Model with Extinction

Waiting Time Distribution for the Emergence of Superpatterns

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Earthquake Forecasting Based on Multi-State System Methodology

Scan Statistics for Detecting a Local Change in Variance for Normal Data with Known Variance

On a Transform Method for the Efficient Computation of Conditional V@R (and V@R) with Application to Loss Models with Jumps and Stochastic Volatility

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Twisting the Alive Particle Filter

Content Provider	Springer Nature Link
Author	Jasr, Ajay Persin, Adam
Copyright Year	2014
Abstract	This work focuses on sampling from hidden Markov models (Cappe et al. 2005) whose observations have intractable density functions. We develop a new sequential Monte Carlo (e.g. Doucet, 2011) algorithm and a new particle marginal Metropolis-Hastings (Andrieu et al J R Statist Soc Ser B 72:269-342, 2010) algorithm for these purposes. We build from Jasra et al (2013) and Whiteley and Lee (Ann Statist 42:115-141, 2014) to construct the sequential Monte Carlo (SMC) algorithm, which we call the alive twisted particle filter. Like the alive particle filter (Amrein and Künsch, 2011, Jasra et al, 2013), our new SMC algorithm adopts an approximate Bayesian computation (Tavare et al. Genetics 145:505-518, 1997) estimate of the HMM. Our alive twisted particle filter also uses a twisted proposal as in Whiteley and Lee (Ann Statist 42:115-141, 2014) to obtain a low-variance estimate of the HMM normalising constant. We demonstrate via numerical examples that, in some scenarios, this estimate has a much lower variance than that of the estimate obtained via the alive particle filter. The low variance of this normalising constant estimate encourages the implementation of our SMC algorithm within a particle marginal Metropolis-Hastings (PMMH) scheme, and we call the resulting methodology “alive twisted PMMH”. We numerically demonstrate, on a stochastic volatility model, how our alive twisted PMMH can converge faster than the standard alive PMMH of Jasra et al (2013).
Ending Page	358
Page Count	24
Starting Page	335
File Format	PDF
ISSN	13875841
e-ISSN	15737713
Journal	Methodology and Computing in Applied Probability
Issue Number	2
Volume Number	18
Language	English
Publisher	Springer US
Publisher Date	2014-08-03
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Life Sciences Economics Alive particle filters Business and Management Approximate Bayesian computation Hidden Markov models Twisted particle filters Sequential Monte Carlo Particle Markov chain Monte Carlo Statistics Electrical Engineering
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability

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